In a case of water ingress, in a drum brake, into a brake drum, or attaching (sticking) of water and mud-water (hereinafter simply called water), in a disc brake, onto a disc rotor, there is a likelihood of taking place shortage of braking effect due to a decrease of frictional coefficient between a brake drum and a brake shoe or between a disc rotor and a brake pad. In some other cases rusting occurring around the wet portions may shorten life of the brake system, or grains of the mud may disadvantageously damage the frictional surfaces. This unfavorable phenomenon also takes place in a drum-in-disc brake which contains both the drum brake portion and the disc brake portion. There have conventionally been proposed some preventing measures, for example, disposing one or another labyrinth (complicated water passage) by means of applying some device or design on the backing plate, dust cover and brake drum, disposing a simple water guard or gutter, etc. All of those have not been satisfactory in the water preventing effect. In addition, the inner brim portion of the dust cover which covers the disc rotor is generally bent inwardly (in the direction approaching the opening portion of the brake drum) for being secured on the outer brim portion of the backing plate which is fixedly disposed in confrontation to the opening portion of the brake drum, and this bent brim portion is likely to introduce water against expectation into the drum brake, to the great disadvantage.